Most of knowledge about Strouhal instability and Von Karman Vortex Street is experimental. Essential basics are exposed in this page.

I - Reynolds number
II - Flow patterns
III - Von Karman Vortex Street




I - Reynolds number

The classical case studied is a cylinder in a laminar flow. Several streams are observable, depending on the Reynolds number. It is defined as:

The Reynolds is the dimensionless number that determines the stability and the flow type. This means that to a given Reynolds number correspond several combinations of the variables, the diameter, the velocity and the fluid. On practical scale, this allows to describe a larger range of Reynolds by varying for instance the diameter instead of the velocity or the fluid.



II - Flow patterns

Depending on the Reynolds, experimental observations show various type of flow pattern described below.

Re<<1 In first case, for the lower Reynolds, the flow is symmetrical upstream and downstream.
Re<4 The symmetry disappears for higher Reynolds and the flow is disturbed in a much longer distance behind the cylinder.
4<Re<40 Re-circulations appear in the wake behind the cylinder for Reynolds about 4. They develop with Reynolds and oscillate for higher Reynolds, creating oscillations in the wake.
40<Re<400 Up to critical Reynolds, about 40, oscillations are so strong that one of the two vortices break away from the cylinder. This is Strouhal instability. The second vortex is shed while the first one is shaped again. The vortices appear and are shed alternatively at a constant frequency. About Reynolds 200, the structure of Von Karman Vortex Street becomes three-dimensional.
400<Re When Reynolds is upper 400, turbulence develop and Von Karman Vortex Street disappears.


III - Von Karman Vortex Street

Frequency determination

The frequency with which vortices are shed behind a circular cylinder in a Karman vortex street is called "n". Experimental measurements show that the dimensionless frequency, called Strouhal number

depends only on the Reynolds number. Experimental results are presented in the followed graph :


Separation

When a region with an adverse pressure gradient exists along the wall, the retarded fluid particles cannot penetrate too far into the region of increased pressure owing to their small kinetic energy. Thus, the boundary layer is deflected sideways from the wall, separates from it, and moves into the main stream : this phenomenon is called separation. The fluid particles behind the point of separation follow the pressure gradient and move in a direction opposite to the external stream.

The point of separation is defined as the limit between forward and reverse flow in the boundary layer in the immediate neighborhood of the wall:

A short distance downstream from the point of separation, the boundary layer becomes so thick that a wake is created


Velocity distribution near the point of separation



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ESPEYRAC Lionel
PASCAUD Stéphane
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Physics Knowledge
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